Can you True Polymorph yourself into an object? Or would doing so break your concentration on the spell?
You lose concentration on a spell if you are incapacitated.
There is nothing that explicitly says you are incapacitated while you are an object, but it is quite clear that you are.
The incapacitated condition says:
An incapacitated creature can't take actions or reactions.
Notably, a creature that is only incapacitated can still use its movement. An object is... just an object - that cannot take actions or reactions. The Dungeon Master's Guide defines an object as:
a discrete, inanimate item.
You are incapacitated, nay, worse than incapacitated - inanimate. And the rules for concentration say:
You lose concentration on a spell if you are incapacitated
So you can true polymorph yourself into an object, but you would immediately drop concentration.
To be clear, this is not RAW in the most strict sense, hence my opening statement: there is nothing that explicitly says you are incapacitated while you are an object.
I find this the relevant part in the true polymorph spell description:
Creature into Object. If you turn a creature into an object, it transforms along with whatever it is wearing and carrying into that form. The creature’s statistics become those of the object, and the creature has no memory of time spent in this form, after the spell ends and it returns to its normal form.
If you have no memory later, that kinda makes concentration impossible. I mean it could be amnesia, but nothing implies that at all.
The transformation lasts for the duration, or until the target drops to 0 hit points or dies. If you concentrate on this spell for the full duration, the transformation lasts until it is dispelled.
This is not unambiguous to me. It might mean that either the end of concentration, dropping to 0 hit points or dying stops the spell (which would be in line with the Duration field), or that the transformation reverts on 0 hp and dying, unless you concentrate, in which case you can keep it up to the full duration, even if the subject died. In the latter case, you can turn yourself into an object, and unless severely damaged, stay that way for the hour.